Known in the art is an internal combustion engine having arranged in an engine exhaust passage an NOx storing and reducing catalyst which stores NOx contained in exhaust gas when the air-fuel ratio of the inflow exhaust gas is lean and releases the stored NOx when the air-fuel ratio of the inflow exhaust gas becomes rich. In this internal combustion engine, the NOx produced when burning fuel under a lean air-fuel ratio is stored in the NOx storing and reducing catalyst. On the other hand, an amount of the stored NOx is calculated, and when the stored NOx amount exceeds a threshold, a rich process, in which the air-fuel ratio of the exhaust gas is temporarily made rich, is performed and thereby the NOx is released from the NOx storing and reducing catalyst and reduced.
In this case, if the calculated amount of the stored NOx is not accurate, the rich process may be performed even though the actual NOx amount is small, and as a result, fuel consumption may increase. If the rich process cannot be performed even though the actual NOx amount is large, and as a result, NOx may pass through the NOx storing and reducing catalyst. Therefore, the stored NOx amount has to be accurately calculated.
From this point of view, there is known an internal combustion engine in which the stored NOx amount is estimated using a polynomial that reflects NOx storing characteristics of the NOx storing and reducing catalyst (See PTL 1.)